WASHINGTON — President Barack Obama expressed frustration Tuesday with the Pentagon’s struggles to cope with sex crimes in the military, saying he expected “consequences” for sex offenders even as a report indicated that the number of sexual assaults increased sharply last year.

“The bottom line is, I have no tolerance for this,” Obama told reporters after he was asked about several recent military scandals, including the weekend arrest of the Air Force’s chief for sexual assault prevention on charges that he groped and attacked a woman in Northern Virginia. “If we find out somebody’s engaging in this stuff, they’ve got to be held accountable, prosecuted, stripped of their positions, court-martialed, fired, dishonorably discharged — period.”

Obama said he had instructed Defense Secretary Chuck Hagel “to step up our game exponentially ” to prevent sex crimes in the military and hold offenders accountable. “For those who are in uniform who’ve experienced sexual assault, I want them to hear directly from their commander in chief that I’ve got their backs,” he added.

Obama’s stern comments came as the Pentagon prepared to release a report showing that the estimated number of military personnel who may have been sexually assaulted rose by nearly one-third over the past two years.

The Pentagon, using anonymous surveys and sampling research, estimated that about 26,000 personnel experienced “unwanted sexual contact” last year, up from about 19,300 in 2010, according to a Defense Department study.

Military officials said they are concerned that most troops may be reluctant to press charges or formally report sexual assault to authorities. The Pentagon recorded 3,374 sexual assault reports last year, compared with 3,192 in 2011, according to a separate report made public Tuesday.

Meanwhile, lawmakers on Tuesday singled out the Air Force for its botched handling of sex crimes, expressing incredulity that the officer in charge of the service’s sexual assault prevention efforts had been arrested for sexual battery.

“This arrest speaks volumes about the status and effectiveness of the Department of Defense’s efforts to address the plague of sexual assaults in the military,” Sen. Carl Levin, D-Mich., chairman of the Senate Armed Services committee, said at a hearing with Air Force leadership.

Gen. Mark Welsh, the Air Force chief of staff, said military lawyers would request jurisdiction in the case involving Lt. Col. Jeffrey Krusinski, the chief of the Air Force’s sexual assault prevention branch. Krusinski was arrested by Arlington County police early Sunday and charged with sexual battery.

Police said Krusinski was drunk about 12:30 a.m. when he approached a woman in a Crystal City parking lot and grabbed her breasts and buttocks. The woman fended off her assailant but “then he attempted to attack her again, and she called 911,” said Dustin Sternbeck, an Arlington police spokesman.

Welsh said he was “appalled” by the arrest and that “it is unacceptable that this occurs anytime or anywhere in our Air Force.” He said that Arlington County prosecutors would make a final decision about whether to grant jurisdiction in the case to the military.

Krusinski is scheduled for arraignment Thursday in Arlington. His booking photo depicted him with a cut under his left eye and contusions on his upper lip. Police said that the victim did not know her attacker.

An Air Force spokeswoman said Krusinski was “removed from his position immediately” as soon as his superiors learned of his arrest Monday.

Efforts to reach Krusinski by email and phone on Tuesday morning were not successful.

Sen. Claire McCaskill, D-Mo., pressed Air Force leaders on whether Krusinski had the proper “credentials” to head the Air Force’s sexual assault prevention branch and if his military record contained any troubling signals.

“Clearly, the accusation is he was drunk and sexually assaulted a stranger in a parking lot,” she said. “It is hard for me to believe” that his record was spotless.

Welsh replied that “there is no indication in [Krusinski’s] professional record or his workplace” that would suggest a problem.

The arrest angered Hagel, who called Air Force Secretary Michael Donley on Monday evening to “express outrage and disgust” and to insist that the matter be dealt with “swiftly and decisively,” according to a Pentagon statement.

The Air Force has acknowledged that it is struggling to contain “a cancer” of sexual assault in the ranks. The service’s leadership has faced heavy scrutiny from lawmakers and advocacy groups over its judgment in handling sex-crime cases, including the rape and assault of dozens of recruits by basic-training instructors at Lackland Air Force Base in Texas.

“Within the Air Force, it has to become unacceptable culturally,” Sen. Angus King, I-Maine, told Welsh and Donley. “The culture is what you have to deal with.”